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arXiv:0901.0790 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Topological phase in two flavor neutrino oscillations

Poonam Mehta

Published May 26, 2009• 37 citations
arXivHTMLPDF

Abstract

We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between nonorthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with $CP$ conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.

DOI
10.1103/physrevd.79.096013

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We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between nonorthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CPCPCP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.
The geometric picture of neutrino oscillations offers a unique way to study the quantum mechanics of this phenomenon. In this picture, the propagation of a neutrino beam is described by a density matrix evolving in a state space with non-trivial geometry. We derive explicit expressions of the mixed state geometric phase which arise during such an evolution for both two and three flavor neutrino oscillations. We show that, in the case of two flavor neutrino oscillations, the geometric phase is independent of the Majorana phase and it can be used as a measure of coherence of the neutrino beam.
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We develop a consistent mathematical framework for studying two flavor neutrino oscillations in presence of non-Hermitian dynamics. We consider two approaches : (a) bi-orthonormal inner product defined by a positive-definite metric operator G\mathcal{G}G and (b) the density matrix prescription by Brody and Graefe [Phys. Rev. Lett. 109, 230405 (2012)]. For the PT\mathcal{PT}PT-symmetric case, we show that the G\mathcal{G}G metric approach does not work well (probabilities are not conserved) both in PT\mathcal{PT}PT-unbroken as well as PT\mathcal{PT}PT-broken regime. Hence, we adopt the density matrix prescription by Brody and Graefe which is a positive semi-definite map. In the density matrix prescription, we note that probability in the steady state limit is not necessarily 1/21/21/2 thereby indicating non-Markovian behavior.
Abstract It is a fundamental question why quantum mechanics employs complex numbers rather than solely real numbers. In this work, we conduct the first analysis of imaginarity quantification in neutrino flavor and spin-flavor oscillations. As quantum systems in coherent superposition, neutrinos are ideal candidates for quantifying imaginarity within the resource theoretic framework, using measures such as the ℓ 1 -norm and the relative entropy of imaginarity. We show that in the case of two-flavor mixing, these measures of imaginarity are nonzero. The measures of imaginarity reach their extreme values when the probabilistic features of quantum theory are fully maximized, i.e., both the transitional and survival probabilities are approximately equal. Our study reveals that the imaginarity, as a resource, can be harnessed not solely from the presence of a complex phase in the mixing matrix but also from the intrinsic quantum dynamics of time evolution itself. We further extend our analysis to explore the dynamics of three-flavor neutrino mixing, incorporating the effects of a nonzero CP phase.
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